FIG. 12 shows a related-art white list inside or outside determining apparatus and method. In a related-art example, a learning unit 121 obtains a subspace transformation formula 123 from a lot of face images for learning by preliminary learning 122. Next, using the subspace transformation formula 123, a feature amount of an image of a person to be registered in a white list input from a registration face input 125 is obtained by registration face feature data extraction 126 and is held in a registration face feature data group 127.
On the other hand, when a face image to be collated is input from a collation face input 129, a feature amount of a face to be collated is extracted by collation face feature data extraction 130, and matching with a feature amount of a face registered in the registration face feature data group 127 is performed by a matching unit 131.
As a result, an identical determining unit 132 determines whether the feature amount of the collation face is identical to the feature amount of a face image of the white list held in the registration face feature data group 127.
Also, Patent Document 1 shows a method for acquiring a feature amount by creating a subspace in consideration of an aging change or by creating subspaces for respective regions of a face, rather than obtaining a feature amount of the entire face.
Further, there is a white list inside or outside determining apparatus capable of authenticating an individual even when a light source changes, by a method (FisherFace) for obtaining an eigenface (PCA) and then minimizing within-class variance and maximizing between-class variance (FLD) and further facilitating calculation of FLD (Non-Patent Document 1).
Hereinafter, PCA (Principal Component Analysis), FLD (Fisher's First Discriminant) and a kernel fisher method described in Non-Patent Document 1 will be described briefly.
PCA is means for reducing dimensionality of image space by a transformation formula in which Mathematical Formula 3 is obtained when N face images are expressed by Mathematical Formula 1 and a variance matrix of images is expressed by Mathematical Formula 2.
                                              ⁢                  {                                                                      x                  1                                                                              x                  2                                                            …                                                                                  x                    N                                    }                                                                                        [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          1                ]                                                          ⁢                              S            T                    =                                    ∑                              K                =                1                            N                        ⁢                                          (                                                      x                    k                                    -                  μ                                )                            ⁢                                                (                                                            x                      k                                        -                    μ                                    )                                T                                                                        [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          2                ]                                          W          PCA                =                              arg            ⁢                                                  ⁢                                          max                W                            ⁢                                                                                    W                    T                                    ⁢                                      S                    T                                    ⁢                  W                                                                              =                      [                                                                                w                    1                                                                                        w                    2                                                                    …                                                                      w                                          m                      p                                                                                            ]                                              [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          3                ]            
Also, FLD is means for minimizing within-person variance and maximizing between-person variance, and a transformation formula of Mathematical Formula 6 is obtained when the between-person variance is expressed by Mathematical Formula 4 and the within-person variance is expressed by Mathematical Formula 5.
                              S          B                =                              ∑                          i              =              1                        C                    ⁢                                                    N                i                            ⁡                              (                                                      μ                    i                                    -                  μ                                )                                      ⁢                                          (                                                      μ                    i                                    -                  μ                                )                            T                                                          [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          4                ]                                          S          W                =                              ∑                          i              =              1                        C                    ⁢                                    ∑                                                x                  k                                ∈                                  X                  i                                                      ⁢                                          (                                                      x                    k                                    -                                      μ                    i                                                  )                            ⁢                                                (                                                            x                      k                                        -                                          μ                      i                                                        )                                T                                                                        [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          5                ]                                          W          FLD                =                  arg          ⁢                                          ⁢                                    max              W                        ⁢                                                                                                W                    T                                    ⁢                                      S                    B                                    ⁢                  W                                                                                                                                  W                    T                                    ⁢                                      S                    W                                    ⁢                  W                                                                                                        [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          6                ]            
Finally, a FisherFace method is a method capable of facilitating calculation of FAD even when the number of images is small, and is expressed by Mathematical Formula 7, Mathematical Formula 8 and Mathematical Formula 9.
                              W          FisherFace          T                =                                            W              fld              T                        ⁢                          W              pca              T                                =                      [                                                                                w                    1                                                                                        w                    2                                                                    …                                                                      w                    c                                                                        ]                                              [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          7                ]                                                          ⁢                              W            fld                    =                      arg            ⁢                                                  ⁢                                          max                W                            ⁢                                                                                                            W                      T                                        ⁢                                          W                      pca                      T                                        ⁢                                          S                      B                                        ⁢                                          W                      pca                                        ⁢                    W                                                                                                                                                  W                      T                                        ⁢                                          W                      pca                      T                                        ⁢                                          S                      W                                        ⁢                                          W                      pca                                        ⁢                    W                                                                                                                            [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          8                ]                                                          ⁢                                            W              pca                        =                          arg              ⁢                                                          ⁢                                                max                  W                                ⁢                                                                                              W                      T                                        ⁢                                          S                      T                                        ⁢                    W                                                                                                  ⁢                                          ⁢                                          ⁢                                    W              fld                        =                          arg              ⁢                                                          ⁢                                                max                  W                                ⁢                                                                                                                        W                        T                                            ⁢                                              W                        pca                        T                                            ⁢                                              S                        B                                            ⁢                                              W                        pca                                            ⁢                      W                                                                                                                                                                  W                        T                                            ⁢                                              W                        pca                        T                                            ⁢                                              S                        W                                            ⁢                                              W                        pca                                            ⁢                      W                                                                                                                                                  [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          9                ]            
Accordingly, dimensionality of WFLD can be reduced to c−1.